Question

if alpha and beta are the roots of the equation 2x²-10x+5 than find the value of (alpha+2) (beta+2)..​

Answer 1

Answer:

(α + 2)(β + 2) = 33/2 = 16.5

Step-by-step explanation:

2x² - 10x + 5 = 0

We know,

α + β = -b/a = -(-10)/2

α + β = 5

Also,

αβ = c/a = 5/2

(α + 2)(β + 2) = (2 + α)(2 + β)

By using identity: (x + a)(x + b) = x² + (a + b)x + ab

a = (2 + α),       b = (2 + β)

(2 + α)(2 + β) = 2² + (α + β)2 + αβ

(2 + α)(2 + β) = 4 + 5(2) + 5/2

(2 + α)(2 + β) = 14 + 5/2

(2 + α)(2 + β) = (28 + 5)/2

(2 + α)(2 + β) = 33/2 = 16.5

(α + 2)(β + 2) = 33/2 = 16.5

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Answer 2

Answer:

the solution of question is in the attachment.